I teach mathematics at Baltimore City College High School, one of the top 2 academic magnet schools in Baltimore, MD. This is my seventh year as a teacher in BCPSS. Prior to that, I graduated from Haverford College, majoring in Mathematics with minors in French and Education. I am currently pursuing my Masters Degree in Math Education from Towson University and expect to graduate in December 2014.
I thoroughly enjoy using technology in the classroom. However, my classroom has many technological challenges. Our school has one mobile laptop cart, but the bandwidth on it is so poor that it takes over half the class period to get all the students logged in. I have 4 desktop computers in my classroom (plus one for my use), but they have to be in the same part of the room, so only a few students can be on them at a time. I generally allow students to use mobile devices for academic purposes when appropriate, but some do not have smartphones, and other students abuse the privilege. I currently use some technological services like Remind101 and twitter to remind students about homework. I also experimented with flipped classroom this year and created a course webpage to support that project.
Many of my students are unaccustomed to using technology to support mathematics learning. I recently assigned a project that asked students to use Excel to create a table and to type their project in Microsoft Word to get them used to typing mathematical symbols. Many students requested explicit instruction on using formulas in Excel and using picture drawing and Equation Editor in Word. While the project was successful overall, it made me realize that students do not know how to find help and also do not know how to experiment with technology. Students can type essays, but balk at using the same program for mathematics work. I will be spending this summer coming up with more such projects (and earlier in the year) to help students become more acclimated to using productivity software for mathematical purposes.
My goals for this course are to learn about new resources and tools that I can implement in the classroom next year to improve my own TPACK and build my students' technological skills while teaching key math content.
Web 2.0 refers to the next generation of websites where users can generate and manipulate the content without having to be the page provider. The initial idea of the World Wide Web was to passively deliver information and content to users, but Web 2.0 tools make the user an active participant in the creation and dissemination of information. Wikis are one of the most common examples of a Web 2.0 tool - anyone can change the content of almost any page at any time!
10.Factor Trees - Useful explanation of and practice with finding the prime factorization of a number. Builds number sense that is needed for simplifying radicals, which is part of extending the properties of exponents to rational exponents (N-RN.1 and N-RN.2).
9.Pan Balance - A simple interface that enables comparison of two expressions. Useful for solving linear equations and inequalities in one variable (A-REI.3), and the graphing window assists students with developing ideas needed for graphing equations on the coordinate plane (A-CED.2).
8.Function Machine - Practice with deriving rules for simple linear functions based on an input-output table. Good review of 8.F.4
7.PlopIt - A visual clicking interface to quickly see the spread of a data set and how it affects the mean, median, and mode. Quickly and easily manipulate the data to manipulate these measures and develop data sets that have given measures of central tendency (S-ID.1, S-ID.2, and S-ID.3).
6.Towers of Hanoi - A fun puzzle that promotes strategic thinking (SMP.1 and SMP.8), but it can also be used to introduce exponential functions (F-LE.2).
5.Function Transformations - The manipulative itself is nothing special, but go through the entire activity to see what happens with each possible transformation of a function (adding a constant, adding a constant to the input, multiplying the function by a constant, etc.). After completing the activity, students will be well versed in how to build new functions from existing functions (F-BF.3)
4.Equation Creations - The "drawing" activity here is fun for students, but it contains a lot of really advanced mathematics for Algebra I (e.g. circular trigonometry). I would recommend assigning as a project with variable outcomes: struggling students can succeed by exploring how changing the variables changes the picture (SMP.4 and SMP.7), while more advanced students can complete all the steps of the interactive to learn more about circular trigonometry (F-TF.2).
3.Algebra Tiles - Slightly more time consuming than physical algebra tiles, but the advantage is that they are not limited in quantity. Additionally, because the tiles align themselves automatically, students will not make errors related to physicality (e.g. gaps in a an array). Useful for teaching factoring of quadratic expressions (A-SSE.3a) and completing the square (A-SSE.3b) as well as solving linear equations in one variable (A-REI.3).
2.Qualitative Grapher - In the real world, functions exhibit different behaviors on different intervals (F-IF.7b). This tool makes it easy to combine functions of different behaviors with a drag-and-drop interface. (F-IF.4 and F-IF.5)
1.Desmos Calculator - One of the most intuitive online graphing calculators with practically every feature you or your students would need. Sliders and set notation support make this tool exceptionally powerful. A must for teaching graphing and solving systems of equations and inequalities (A-REI.10) and for introducing general functions (F-IF.4, F-IF.5, and F-IF.7).
Lesson Brief #1
After watching the video The 100 Meter Dash and being given a list of the data it is based on, students will work in groups to create mathematical models that describe the change in winning times in this event over time. Students will discuss the mathematical features of their model to answer questions like:
Based on your model, what will the winning time be in the 2016 Olympics? The 2100 Olympics? The 3000 Olympics? Are these answers reasonable?
Based on your model, when will the winning time be under 9 seconds? Under 7 seconds? Under 1 second? Do these answers impact the reliability of your model?
Why did you select the type of function you did for this model? Is there another type of function that might be more reasonable?
Lesson Brief #2
After watching the video The 100 Meter Dash and the first two minutes of the video The Long Jump, students will compare and contrast the results of how winning times/distances have changed over time. Specifically, students will conjecture why winning distances in the Long Jump have not increased over time in the same manner that winning times in the 100 Meter Dash have consistently decreased over time. Students will brainstorm variables that may affect the Long Jump results differently than the 100 Meter Dash. After developing a list of variables, students will watch the last minute of the Long Jump movie. Students will then research information about the winning long jumpers and their distances and use technology to create a multi-variable model to predict winning distances. Students will also be asked to describe what non-quantitative variables are being represented by the year in the model.
Suppose there is an island in the center of a pond. There is one bridge that connects the island to the shore. (See diagram below) On the island is a treasure chest with $1,000,000. You can select either Nathan Adrian (swimmer) or Usain Bolt (runner) to retrieve the chest for you - whoever reaches the island first will win it. Both athletes will start from the same place - Adrian will swim directly to the island, while Bolt will have to run along the edge of the pond to the bridge and then over the bridge to the island. Explain whom you would select to win and why. Your answer may depend on (1) where the starting point is, (2) the radius of the pond, and (3) other real-world factors not otherwise mentioned. State explicitly what assumptions you made to answer the question. How would your answer change if Usain Bolt were required to only run in a clockwise direction to the bridge (instead of taking the shortest path)?
I personally did not like Educreations - I wanted something with more options and power. I used Screencast-o-Matic last year, and that was fine. I now have a Wacom Tablet, so that will make my videos better this year. However, while it isn't free, Camtasia Studio is kind of awesome for educational videos (especially with the quizzing feature built in).
Bio
I teach mathematics at Baltimore City College High School, one of the top 2 academic magnet schools in Baltimore, MD. This is my seventh year as a teacher in BCPSS. Prior to that, I graduated from Haverford College, majoring in Mathematics with minors in French and Education. I am currently pursuing my Masters Degree in Math Education from Towson University and expect to graduate in December 2014.
Learning Task #1
SAMR Model Prezi
Reflection for Learning Task #1
I thoroughly enjoy using technology in the classroom. However, my classroom has many technological challenges. Our school has one mobile laptop cart, but the bandwidth on it is so poor that it takes over half the class period to get all the students logged in. I have 4 desktop computers in my classroom (plus one for my use), but they have to be in the same part of the room, so only a few students can be on them at a time. I generally allow students to use mobile devices for academic purposes when appropriate, but some do not have smartphones, and other students abuse the privilege. I currently use some technological services like Remind101 and twitter to remind students about homework. I also experimented with flipped classroom this year and created a course webpage to support that project.
Many of my students are unaccustomed to using technology to support mathematics learning. I recently assigned a project that asked students to use Excel to create a table and to type their project in Microsoft Word to get them used to typing mathematical symbols. Many students requested explicit instruction on using formulas in Excel and using picture drawing and Equation Editor in Word. While the project was successful overall, it made me realize that students do not know how to find help and also do not know how to experiment with technology. Students can type essays, but balk at using the same program for mathematics work. I will be spending this summer coming up with more such projects (and earlier in the year) to help students become more acclimated to using productivity software for mathematical purposes.
My goals for this course are to learn about new resources and tools that I can implement in the classroom next year to improve my own TPACK and build my students' technological skills while teaching key math content.
Learning Task #2
Today's Meet Room
Mr. Colvin's Kidblog
What is Web 2.0?
Web 2.0 refers to the next generation of websites where users can generate and manipulate the content without having to be the page provider. The initial idea of the World Wide Web was to passively deliver information and content to users, but Web 2.0 tools make the user an active participant in the creation and dissemination of information. Wikis are one of the most common examples of a Web 2.0 tool - anyone can change the content of almost any page at any time!
Learning Task #3
Glogster - Solving Systems of Equations by Substitution
Prezi - Mean, Median, and Mode
Learning Task #4
Top 10 Virtual Manipulatives for Algebra I
10. Factor Trees - Useful explanation of and practice with finding the prime factorization of a number. Builds number sense that is needed for simplifying radicals, which is part of extending the properties of exponents to rational exponents (N-RN.1 and N-RN.2).
9. Pan Balance - A simple interface that enables comparison of two expressions. Useful for solving linear equations and inequalities in one variable (A-REI.3), and the graphing window assists students with developing ideas needed for graphing equations on the coordinate plane (A-CED.2).
8. Function Machine - Practice with deriving rules for simple linear functions based on an input-output table. Good review of 8.F.4
7. PlopIt - A visual clicking interface to quickly see the spread of a data set and how it affects the mean, median, and mode. Quickly and easily manipulate the data to manipulate these measures and develop data sets that have given measures of central tendency (S-ID.1, S-ID.2, and S-ID.3).
6. Towers of Hanoi - A fun puzzle that promotes strategic thinking (SMP.1 and SMP.8), but it can also be used to introduce exponential functions (F-LE.2).
5. Function Transformations - The manipulative itself is nothing special, but go through the entire activity to see what happens with each possible transformation of a function (adding a constant, adding a constant to the input, multiplying the function by a constant, etc.). After completing the activity, students will be well versed in how to build new functions from existing functions (F-BF.3)
4. Equation Creations - The "drawing" activity here is fun for students, but it contains a lot of really advanced mathematics for Algebra I (e.g. circular trigonometry). I would recommend assigning as a project with variable outcomes: struggling students can succeed by exploring how changing the variables changes the picture (SMP.4 and SMP.7), while more advanced students can complete all the steps of the interactive to learn more about circular trigonometry (F-TF.2).
3. Algebra Tiles - Slightly more time consuming than physical algebra tiles, but the advantage is that they are not limited in quantity. Additionally, because the tiles align themselves automatically, students will not make errors related to physicality (e.g. gaps in a an array). Useful for teaching factoring of quadratic expressions (A-SSE.3a) and completing the square (A-SSE.3b) as well as solving linear equations in one variable (A-REI.3).
2. Qualitative Grapher - In the real world, functions exhibit different behaviors on different intervals (F-IF.7b). This tool makes it easy to combine functions of different behaviors with a drag-and-drop interface. (F-IF.4 and F-IF.5)
1. Desmos Calculator - One of the most intuitive online graphing calculators with practically every feature you or your students would need. Sliders and set notation support make this tool exceptionally powerful. A must for teaching graphing and solving systems of equations and inequalities (A-REI.10) and for introducing general functions (F-IF.4, F-IF.5, and F-IF.7).
Learning Task #5
Student Information Form 2014
Teacher Technology Use Survey
Learning Task #6
Function Families Text-2-MindMap
Mr. Colvin's Parking Lot Padlet
Motivation and Attribution Theories Popplet (in progress)
Learning Task #7
Lesson Brief #1
After watching the video The 100 Meter Dash and being given a list of the data it is based on, students will work in groups to create mathematical models that describe the change in winning times in this event over time. Students will discuss the mathematical features of their model to answer questions like:
Lesson Brief #2
After watching the video The 100 Meter Dash and the first two minutes of the video The Long Jump, students will compare and contrast the results of how winning times/distances have changed over time. Specifically, students will conjecture why winning distances in the Long Jump have not increased over time in the same manner that winning times in the 100 Meter Dash have consistently decreased over time. Students will brainstorm variables that may affect the Long Jump results differently than the 100 Meter Dash. After developing a list of variables, students will watch the last minute of the Long Jump movie. Students will then research information about the winning long jumpers and their distances and use technology to create a multi-variable model to predict winning distances. Students will also be asked to describe what non-quantitative variables are being represented by the year in the model.
Lesson Brief #3
After watching the videos The 100 Meter Freestyle and The 100 Meter Dash, students will be asked the following question:
Suppose there is an island in the center of a pond. There is one bridge that connects the island to the shore. (See diagram below) On the island is a treasure chest with $1,000,000. You can select either Nathan Adrian (swimmer) or Usain Bolt (runner) to retrieve the chest for you - whoever reaches the island first will win it. Both athletes will start from the same place - Adrian will swim directly to the island, while Bolt will have to run along the edge of the pond to the bridge and then over the bridge to the island. Explain whom you would select to win and why. Your answer may depend on (1) where the starting point is, (2) the radius of the pond, and (3) other real-world factors not otherwise mentioned. State explicitly what assumptions you made to answer the question. How would your answer change if Usain Bolt were required to only run in a clockwise direction to the bridge (instead of taking the shortest path)?
LearnZillion vs. Khan Academy
LearnZillion Sample Lessons
Pros
Cons
Khan Academy Sample Lessons
Pros
Cons
Learning Task #8
Solving One-Variable Equations
Introduction to Logarithms
I personally did not like Educreations - I wanted something with more options and power. I used Screencast-o-Matic last year, and that was fine. I now have a Wacom Tablet, so that will make my videos better this year. However, while it isn't free, Camtasia Studio is kind of awesome for educational videos (especially with the quizzing feature built in).
Learning Task #9
Poll Everywhere Poll
TestMoz Test
Learning Task #10
Mobile Apps Prezi
Web 2.0 Tool Project